This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A283301 #14 Jan 03 2025 03:15:13
%S A283301 0,1,1,1,1,1,691,2,3617,43867,174611,155366,236364091,1315862,
%T A283301 3392780147,6892673020804,7709321041217,151628697551,
%U A283301 26315271553053477373,308420411983322,261082718496449122051,3040195287836141605382,2530297234481911294093
%N A283301 Numerators of coefficients at even powers in Taylor series expansion of log(x/sin(x)).
%C A283301 This sequence shares many terms with A046988 (and appears to have been erroneously confused with it), but actually differs from it at indexes 0, 14, 22, 26, 28, 30, 38, 42, 44, 46, 50, 52, 54, 56, 58, 60, ...
%D A283301 L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205
%D A283301 T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 222, series for log(H(x)/x).
%D A283301 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
%D A283301 CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.
%D A283301 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 32, equation 32:6:4 at page 301.
%F A283301 log(x/sin(x)) = Sum_{n>0} (2^(2*n-1)*(-1)^(n+1)*B(2*n)/(n*(2*n)!) * x^(2*n)). - _Ralf Stephan_, Apr 01 2015 [corrected by _Roland J. Etienne_, Apr 19 2016]
%e A283301 log(x/sin(x)) = (1/6)*x^2 + (1/180)*x^4 + (1/2835)*x^6 + (1/37800)*x^8 + (1/467775)*x^10 + (691/3831077250)*x^12 + ...
%t A283301 a[0] = 0; a[n_] := Numerator[((-1)^(n + 1) 2^(2 n - 1) BernoulliB[2 n])/(n (2 n)!)]; Table[a[n], {n, 0, 20}] (* or *)
%t A283301 Numerator@Table[SeriesCoefficient[Log[x/Sin[x]], {x, 0, 2n}], {n, 0, 20}]
%Y A283301 Cf. A046989 (denominators), A046988.
%K A283301 nonn,frac,nice
%O A283301 0,7
%A A283301 _Vladimir Reshetnikov_, Mar 04 2017